Two Inhibitors, One Substrate: Reading an Enzyme Kinetics Table
An undergraduate lab measures alkaline phosphatase activity with p-nitrophenyl phosphate (pNPP) and follows product formation at 405 nm. Initial rates (micromoles of product per minute) were measured in triplicate at seven substrate concentrations with no inhibitor, with 10 micromolar inhibitor A, and with 10 micromolar inhibitor B. Both inhibitors were dissolved in DMSO: final DMSO was 1% in inhibited reactions and 0% in uninhibited reactions. Compound B is an intensely yellow dye. Mean rates:
| [pNPP] (mM) | 0.05 | 0.10 | 0.25 | 0.50 | 1.0 | 2.0 | 5.0 |
|---|---|---|---|---|---|---|---|
| No inhibitor | 4 | 8 | 16 | 25 | 33 | 40 | 44 |
| + Inhibitor A | 2 | 4 | 9 | 16 | 25 | 33 | 40 |
| + Inhibitor B | 2 | 4 | 8 | 12 | 17 | 20 | 22 |
1. Classify each inhibitor from the data, showing the quantitative reasoning rather than relying on definitions.
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Method: compare the inhibited/uninhibited ratio across the substrate range. A single substrate concentration cannot distinguish inhibition types, because many mechanisms halve the rate at low [S]. The discriminating signal is what happens as [S] becomes saturating.
| [pNPP] (mM) | 0.05 | 1.0 | 5.0 |
|---|---|---|---|
| Ratio, A | 0.50 | 0.76 | 0.91 |
| Ratio, B | 0.50 | 0.52 | 0.50 |
Inhibitor A - competitive.
- Inhibition is strong at low [S] and nearly abolished at high [S]; the rate approaches the uninhibited maximum (40 vs. 44 at 5 mM, still rising toward about 45-46).
- Apparent Vmax is unchanged, apparent Km increases. Substrate and inhibitor compete for the same site, so raising [S] outcompetes the inhibitor.
Inhibitor B - noncompetitive (pure).
- The ratio is flat at about 0.50 across a 100-fold substrate range: Vmax is halved, Km is unchanged.
- The inhibitor binds a site other than the substrate site and reduces the catalytic capacity of the enzyme; extra substrate does not help.
2. Predict what happens to each inhibited reaction if substrate is raised to 10 mM, and explain the molecular basis and the practical implication for drug design.
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Prediction
- Inhibitor A: rate rises to nearly the uninhibited Vmax (about 46 umol/min) - inhibition is surmountable.
- Inhibitor B: rate plateaus near 22 umol/min - a ceiling at half of Vmax that no amount of substrate can lift.
Molecular basis
- A occupies the active site reversibly. At any instant the fraction of enzyme bound by A depends on the relative concentrations and affinities of A and substrate; flooding the system with pNPP shifts the equilibrium toward the enzyme-substrate complex.
- B binds elsewhere and, once bound, lowers turnover (or removes that fraction of enzyme from the active pool). Adding substrate does not displace B, so the ceiling persists.
Practical implication
- For a competitive inhibitor used as a drug, potency depends on the local substrate concentration. In a tissue where substrate is high, the drug may look useless even at good affinity; raising the dose can help.
- For a noncompetitive inhibitor, efficacy is independent of substrate level, so potency tracks inhibitor concentration and enzyme turnover rather than substrate flux.
- Reporting only a percent inhibition at one substrate concentration would have made A and B (both ~50%) look identical.
3. A reviewer objects to the experiment as run. Identify the missing controls and state, for each, the direction in which the artifact would bias the conclusion.
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1. Missing vehicle control (DMSO).
- Uninhibited reactions contained 0% DMSO while inhibited reactions contained 1%. If DMSO alone reduces alkaline phosphatase activity, part of the "inhibition" assigned to A and B is actually solvent effect.
- Bias: overestimates inhibition, i.e., makes both compounds look more potent than they are. Fix: 1% DMSO in the no-inhibitor wells; if DMSO alone inhibits, use the DMSO-only rate as the baseline.
2. Missing inhibitor-only blank.
- Compound B is yellow and absorbs at 405 nm, the same wavelength used to quantify p-nitrophenol. Absorbance from B adds to the product signal.
- Bias: the measured rate for B is too high, so true inhibition by B is greater than the table shows - the qualitative classification (noncompetitive) survives, but the magnitude does not. A no-enzyme blank containing B at each concentration must be subtracted, and the absorbance spectrum of B checked for overlap with the product peak.
3. Other checks
- Confirm rates are initial (linear with time) and that substrate is not depleted, especially at low [S].
- Include a product standard curve to convert absorbance to micromoles, and verify enzyme concentration is in the linear range.
- If either artifact moves the numbers, rerun before assigning a mechanism; a flat ratio of 0.50 with a corrected baseline could shift toward a different inhibition model.